This question seems to stump students from coast to coast. Most seem to know what the SAT is, but the PSAT is a bit murky (especially since mock SAT tests are widely called PSATs, a misnomer that doesn't help the confusion). Let's start with the SAT.
The SAT is administered seven times a year (check out test dates here). The SAT is the "official" test; in other words, the one you will be eventually submitting to colleges. You will be tested on critical reading, math and writing, including one essay. The test takes close to four hours to complete, and they are always administered on Saturday (unless you are taking it on Sunday for religious reasons). You will take the SAT at a test center, not at your high school. You can find specifics from the College Board here.
Now for the much more confusing PSAT. Many students think that the PSAT is any practice SAT they may take during the year, administered by their school, test prep company, etc. This is not true! There is an official PSAT, which is administered only once a year in October. You will take the test at your high school, either on a Wednesday or a Saturday. The PSAT is intended to be a practice SAT, and many students take it in both their sophomore and junior years of high school. The PSAT format is shorter than the SAT, taking only a little more than two hours to complete. Otherwise, the types of questions are exactly like those on the SAT. But most students like to learn there is no essay on the PSAT! It's also good news for most students that the PSAT is essentially a "freebie," and your scores are not reported to colleges. You can really think of it as a practice SAT. For a few high scoring juniors, the PSAT is also the qualifying test for the National Merit Scholarship competition, but you probably already knew that if you're shooting for a high score. The last bit of confusion over the PSAT is the scoring. Unlike the SAT, your score will not end in zero. But to compare to the SAT, just add zeros to your scores!
So there you have it. The SAT is long, has an essay, and "counts" in the college admissions process. The PSAT is shorter, has no essay, and for the vast majority of students it's simply a practice test for the SAT. As for all those practice tests you may be taking as part of your test prep, they are simply that, practice SATs.